Circles - Area, Circumference, Radius & Diameter Explained! - Free Educational videos for Students in K-12 | Lumos Learning

Circles - Area, Circumference, Radius & Diameter Explained! - Free Educational videos for Students in k-12


Circles - Area, Circumference, Radius & Diameter Explained! - By The Organic Chemistry Tutor



Transcript
00:0-1 in this video , we're going to talk about how
00:02 to calculate the area and the circumference of a circle
00:07 . But first let's talk about the radius and the
00:10 diameter of a circle . My drawing is not perfect
00:13 , but we're gonna make the best of that .
00:16 So here is the center of the circle . It's
00:19 a point right at the middle of the circle .
00:23 Now the distance between the center of the circle and
00:25 any point on a circle that is known as the
00:29 radius of the circle , the diameter is twice the
00:37 value of the radius . Yeah . So let's say
00:40 this is the center of the circle . The diameter
00:45 starts from one end of the circle , it passes
00:48 through the center and connects to the other end of
00:50 the circle . So as you can see visually it's
00:56 twice as long as the radius of the circle .
01:00 So we can say that D is equal to to
01:06 our . Now the next thing need to be familiar
01:13 with is the area and its circumference of a circle
01:19 . The area is basically the area of the shaded
01:22 region . To calculate the area of a circle ,
01:29 you could use this formula . It's Pie times are
01:32 squared . Now the circumference is basically the distance around
01:40 the edge of the circle . So this is the
01:42 circumference . And to calculate the circumference it's equal to
01:46 two pi times are Now pie is equal to 3.14
01:56 , 159 2654 . And there are more other numbers
02:02 , you know that go on after that . But
02:06 typically when solving these problems in school , you'll be
02:09 using approximate value of pi , Which is usually 3.14
02:15 . So now let's work on some problems . Let's
02:19 start with this one , number one , calculate the
02:22 area and circumference of the circle shown below . Use
02:26 Pi equals 3.14 . So let's start with the area
02:32 . The area is equal to pi r squared The
02:40 radius . We can clearly see that the radius of
02:43 this circle is five ft . It's the distance between
02:46 the center and the point on the circle . So
02:51 we have pie times five ft squared , five squared
02:59 is five times five , which is 25 and feet
03:03 times feet gives you square feet . So the units
03:06 of area is always square units square inches , square
03:09 feet , square yards and so forth . Now the
03:15 exact answer for the area of the circle is 25
03:19 pi square feet . But we're going to get an
03:25 approximation using this value . So let's replace pie With
03:34 3.14 . So the answer for this problem , the
03:46 area is approximately 78.5 square feet . So that's how
03:55 you can calculate the area of a circle . If
03:59 you're given the radius of that circle , now let's
04:03 move on to the second part of the problem ,
04:06 let's calculate the circumference of the circle . So we're
04:11 gonna use the formula C . Is equal to two
04:13 pi R Let's get the exact valley 1st . So
04:22 let's replace the radius with five ft . two pi
04:27 times five is 10 pie . So the exact answer
04:30 is 10 pie feet . So notice that the unit
04:34 for circumference is in feet , which is the same
04:37 as unit for radius , but the unified area is
04:40 in square feet . Now let's replace pie with 3.14
04:47 . So this will give us an approximate answer 10
04:54 times 3.14 , It's going to be 31.4 . So
04:59 the circumference of this particular circle is 31.4 feet .
05:06 So if you were to start here , let's say
05:08 on a track and you would let's see where to
05:11 walk around in this circle , You would travel a
05:15 distance of 31.4 ft . So that's what that means
05:20 , Given that The radius of the circle is five
05:23 ft . Now let's work on a similar problem at
05:30 this time . Were given the diameter of the circle
05:34 , the diameter is 14 inches . How can we
05:39 use the diameter to calculate the area and the circumference
05:42 of the circle ? Well , the first thing we
05:45 need to do is we need to find the radius
05:47 . Remember the diameter is twice the length of the
05:51 radius . So if we divide both sides of this
05:54 equation by two we'll get that . The radius is
05:58 half of the diameter , Half of 14 or 14
06:04 divided by two is 7 . So the radius of
06:06 this circle is 7" . So now that we know
06:11 the radius of the circle , we can calculate the
06:13 area and the circumference . So let's start with the
06:16 area , we know the area is pi R squared
06:23 . So let's replace our with seven inches seven squared
06:31 or seven times 7 is 49 . So we get
06:34 that the area is 49 pi square inches . So
06:40 this right here is the exact answer . But now
06:45 let's replace pie with 3.14 49 times 3.14 . That's
07:00 1 53.86 . But what we're gonna do is we're
07:05 going around our answer to 154 square inches . So
07:15 that's the area of the circle in this problem .
07:21 Now let's calculate the circumference . The circumference is two
07:28 pi r . Let's replace our with 7" . So
07:37 we have two pi times seven . So we get
07:41 an exact answer of 14 pie inches . Now let's
07:47 get our approximate answer by replacing pie With 3.14 14
08:02 times 3.14 , That's 43.96 . But since we use
08:08 3.14 for pie , I'd like to run my answer
08:11 to three significant figures . So I'm going around it
08:15 to 44.0 inches . So that's the approximate value for
08:26 the circumference of the circle . Number two . The
08:30 area of a circle is 28.5 sq in . What
08:35 is the radius of the circle ? So we're gonna
08:38 use 3.14 for pi . We're gonna run our answer
08:41 to the nearest 10th place . So let's start with
08:47 this form of area is equal to pi R squared
08:53 . So we're gonna replace the area with 28.5 sq
08:57 in . And we're going to replace pie with 3.14
09:01 . We're gonna solve for R . In order to
09:05 do that , we need to divide both sides ,
09:07 Bye 3.14 . So we get 28.5 divided by 3.14
09:19 . And that works out to be 9.07 64 3
09:26 3 with some of the numbers . But this should
09:28 be good enough so that is equal to r squared
09:31 to get our we need to take the square root
09:33 of both sides , So the square root of 9.076433
09:44 . We could around the answer . So let's use
09:49 are approximate symbol . So we're gonna round it to
09:52 3.01 . So that's the nearest 100th . So this
09:58 is the radius of the circle . That's how we
09:59 could find it . If we're given the area of
10:02 the circle . And by the way , let's not
10:04 forget the unit for radius . The unified area is
10:09 square inches . So the unit for the radius of
10:12 this circle is going to be just inches . The
10:15 radius diameter circumference . They have units like inches ,
10:20 feet , yards , Things like that area is always
10:23 square units , so just keep that in mind .
10:25 But these two , they must match number three .
10:32 The circumference of a circle is 14.5 ft . What
10:36 is the diameter of the circle ? So the formula
10:42 that we need to use is circumference is equal to
10:45 two pi r . Now what we need to do
10:48 here is we need to use the circumference to calculate
10:51 the radius of the circle . Once we have the
10:54 radius of the circle , we could then find the
10:56 diameter of the circle because we know that the diameters
10:59 twice the value of the radius of the circle .
11:01 So let's calculate our furs . Let's replace C with
11:05 14.5 ft . Unless you place pie With 3.14 Two
11:16 times 3.14 , that's 6.28 . So they get our
11:22 by itself , we need to divide both sides by
11:26 6.28 , 14.5 , divided by 6.28 . We get
11:37 2.3089 . We're going around it to the nearest 10th
11:41 , I mean to the nearest 100 . So that's
11:43 going to be two 31 Now let's put the units
11:50 . So the universe circumference is in feet . That's
11:53 gonna be the same for the unit of radius .
11:57 So now that we have the radius , we could
11:59 find the diameter , the diameter is simply to our
12:03 it's twice the value of art , So it's going
12:08 to be two times 2.31 , two times 2 is
12:14 four , two times 31 is 62 . So the
12:20 diameter of this circle is gonna be approximately 4.62 ft
12:25 . Number four . The circumference of a circle is
12:28 18 pie m . What is the area of the
12:31 circle ? Go ahead and try that problem . So
12:40 let's begin with this equation , C . Is equal
12:42 to two pi R . So that's our circumference equation
12:47 . And we also know that the area is pi
12:50 R squared . So those are the two equations that
12:53 we have . So we're given the circumference and we
12:57 need to find in the area . What we need
13:00 to do is we need to use the circumference to
13:01 get the radius once we have the radius , we
13:04 could plug it into the second equation to get the
13:06 area . So let's go ahead and do that .
13:10 So we're gonna replace the circumference with what it equals
13:14 18 pie meters . Now we're going to solve for
13:21 r To get our by itself , we need to
13:23 divide both sides by two pi on the right side
13:29 to Pie will cancel . On the left side .
13:32 Pie will cancel . And we're going to have 18
13:34 divided by two , which is nine . So this
13:38 is the radius of the circle , it's nine .
13:42 And since the unit for circumference is in meters ,
13:45 the radius is going to be in meters as well
13:48 . So this is an exact answer . So now
13:52 let's use that to calculate the area . So let's
13:56 replace our with nine m nine Squared is 81 .
14:01 So the exact answer for the area will be 81
14:04 pie square meters . Now , let's get our approximate
14:09 answer . Let's replace pie With 3.14 . So 81
14:22 times 3.14 . That's 254.34 . So we're going to
14:29 round that to the nearest whole number , Which will
14:32 be 254 . So that's the approximate area of the
14:37 circle . It's 200 54 square meters . That's the
14:43 answer number five . The area of a circle is
14:48 100 square yards . What is the circumference of the
14:51 circle ? So let's write the two equations that we're
14:57 going to use A is equal to pi R ,
15:00 squared and C is equal to two pi R .
15:05 So this problem is basically the reverse of the previous
15:08 problem . Were given the area . We're going to
15:10 use that to calculate our once we have our we're
15:13 going to plug it into this equation to get the
15:15 circumference . So let's replace A with 100 square yards
15:24 And let's plug in Pi as 3.14 . So to
15:30 get our by itself , what we're gonna do is
15:31 we're gonna divide both sides By 3.14 100 , divided
15:40 by 3.14 . That is 31 eight 47 133 And
15:49 that square yards . So to get our we need
15:54 to take the square root of both sides . So
16:01 the square root of 31.847133 , that's 5.6433 three .
16:15 And the square root of yards square . It is
16:18 just yards . So this is the approximate valley for
16:23 the radius . So now we're gonna take that answer
16:26 and plug it in to the circumference equation . So
16:30 we have C is equal to two pi but we're
16:32 gonna use 3.14 for pi and then we're gonna replace
16:36 our with 5.6433 , 3 yards . So you should
16:55 get 35.440 . But we're going to round it to
16:59 the nearest 10th . So we're going to say that
17:01 the circumference is approximately 35.4 and the unit is going
17:08 to be yards . So that's how you can calculate
17:11 the circumference if you know the area of the circle
17:14 . And that's basically it for this video . Thanks
17:17 for watching
Summarizer

DESCRIPTION:

This basic geometry video tutorial explains how to calculate the area and circumference of a circle given it's radius and diameter. This video contains a few examples with word problems. This video also explains how to calculate the circumference given the area, and how to calculate

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Circles - Area, Circumference, Radius & Diameter Explained! is a free educational video by The Organic Chemistry Tutor.

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